6. Subtract 7/2 of third row from first and 9/5 of it from second
row:

A =

1

3/2

0

0

1

0

0

0

1

V =

1

0

0

7. Substitute for y in the first equation:

x = 1
y = 0
z = 0

7. Subtract 3/2 of 2nd row from 1st:

A =

1

0

0

0

1

0

0

0

1

V =

1

0

0

You see, if you follow this example, that solving equations by systematically
eliminating variables, and using Gaussian elimination to change a matrix into
the identity matrix are essentially the same thing.